Skip to content
GitLab
Menu
Projects
Groups
Snippets
/
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Sebastian Steinlechner
pykat
Commits
121fe5fc
Commit
121fe5fc
authored
Aug 11, 2015
by
Daniel Brown
Browse files
Merge branch 'master' of gitmaster.atlas.aei.uni-hannover.de:pykat/pykat
parents
9212e608
06194b20
Changes
2
Expand all
Hide whitespace changes
Inline
Side-by-side
pykat/maths/zernike.py
View file @
121fe5fc
import
numpy
as
np
from
scipy.misc
import
factorial
as
fac
import
math
def
zernike_R
(
m
,
n
,
rho
):
...
...
@@ -36,3 +37,75 @@ def zernike(m, n, rho, phi):
else
:
return
zernike_R
(
0
,
n
,
rho
)
def
znm2Rc
(
A
,
R
):
'''
Convertes amplitudes of Zernike polynomials of order n=2 into
spherical radius of curvature. In case the astigmatic modes
(m=-1,m=2) are included, the functon returns the maximum and
minimum curvature.
Inputs: A, R
A - List of amplitudes of order 2 Zernike polynomials, ordered so that m
increases with list index. 1 <= len(A) <= 3. [m]
R - Radius of the mirror surface in the xy-plane. [m]
Returns: Rc
Rc - If astigmatic modes are used (len(A) == 2 or 3) a numpy.array of length
2 containing max and min curvatures is returned. If only the 'defocus'
mode is used Rc is a float number. [m]
Based on the Simtools function 'FT_Znm_to_Rc.m' by Charlotte Bond.
'''
if
isinstance
(
A
,
list
):
if
len
(
A
)
==
3
:
a20
=
A
[
1
]
a22
=
math
.
sqrt
(
A
[
0
]
**
2
+
A
[
2
]
**
2
)
s
=
np
.
array
([
1.0
,
-
1.0
])
elif
len
(
A
)
==
2
:
a20
=
0
a22
=
math
.
sqrt
(
A
[
0
]
**
2
+
A
[
1
]
**
2
)
s
=
np
.
array
([
1.0
,
-
1.0
])
elif
len
(
A
)
==
1
:
a20
=
A
[
0
]
a22
=
0
s
=
0
elif
isinstance
(
A
,
float
)
or
isinstance
(
A
,
int
):
a20
=
A
a22
=
0
s
=
0
Rc
=
((
2
*
a20
+
s
*
a22
)
**
2
+
R
**
2
)
/
(
2
*
(
2
*
a20
+
s
*
a22
))
return
Rc
def
Rc2znm
(
Rc
,
R
):
'''
Converts Radius of curvatue to amplitudes of the second order Zernike
polynomials.
Iputs: Rc, R
Rc - Radius of curvature. Either a number or a numpy.ndarray with
minimum and maximum curvature.
R - Radius of mirror in xy-plane.
Returns: A
A - Ampltude(s) of the second order Zernike polynomials needed. Is
a number if Rc is a number, and if R is a numpy.ndarray so is A.
Based on Simtools function 'FT_Rc_to_Znm.m' by Charlotte Bond.
'''
# Amplitude in x and y directions
c
=
(
Rc
-
np
.
sign
(
Rc
)
*
np
.
sqrt
(
Rc
**
2
-
R
**
2
)
)
/
2
if
isinstance
(
Rc
,
np
.
ndarray
):
A
=
np
.
array
([])
# Adding Z(2,0) amplitude
A
=
np
.
append
(
A
,
c
.
mean
())
# Adding Z(2,2) amplitude
A
=
np
.
append
(
A
,
2
*
(
c
[
0
]
-
A
[
0
]))
elif
isinstance
(
Rc
,
float
)
or
isinstance
(
Rc
,
int
):
A
=
c
return
A
pykat/optics/maps.py
View file @
121fe5fc
This diff is collapsed.
Click to expand it.
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment